It's a discretionary act on his part. He's not required to decorate the rotunda at all, but once he does, it cannot be exclusive to his particular viewpoint in matters of religion. If he had chosen to decorate the rotunda in a secular manner, he could have done so in whatever manner he sees fit without ever implicating the establishment clause, which has been the source of his troubles from the beginning - nothing in the First Amendment prevents Judge Moore from using his office to stake out a position on secular issues, after all. Indeed, his job requires him to do exactly that. But once religion becomes the subject, the establishment clause comes into play, and Judge Moore has less of a free hand than he might otherwise wish for, by virtue of the fact that he's an agent of the state.
This is starting to get away from the question I asked at #1071: "Is it truly one of the 'privileges' of citizens to put whatever religious decoration they want in their courthouses & other government buildings?" You began to address it, but now you're moving away from it again. The argument you gave me in the paragraph above can only be completed by saying how it affects the liberties of the individual. As I said earlier, prohibiting all people from putting up religious displays is just as unacceptable as prohibiting some people. You appeared to agree with me, I think.
So how does it more adversely affect the liberties of the individual when Moore puts up the Decalogue while excluding other displays, vs. him putting up nothing while excluding other displays? The individual citizens are just as restricted either way.